The 24-year-old joined the Red Devils from Dortmund in the summer of 2012 having won the Bundesliga title with Jurgen Klopp's side, but has found it tough to hit similar heights since making the move to England.
Kagawa has again been used sparingly by David Moyes, having found himself in and out of the team under former manager Sir Alex Ferguson, but the Japan international is determined to turn the corner and get over what he describes as a "mental block".
|MAN UNITED LATEST
|2/1||Shinji Kagawa is 2/1 with Bet365 to score for Manchester United against Fulham|
"I pressure myself to score in every game but some days it feels like I just can't win. I know I have to overcome that; actually if I can't it really shows that I haven't grown as a player. So because of that I have to really focus on the second half of the season and overcome that mental block."
Despite his struggles, Kagawa has featured in five of the club's six Champions League group games this term and he hopes that United can defeat Olympiakos and set-up a potential quarter-final tie with Dortmund or Barcelona.
He added: "Last year we lost to Real Madrid so this time we want to beat Olympiakos and reach the quarter-finals. Of course our goal is to reach the final and to win the championship. The whole world watches [the Champions League] and it's the top club competition in the world.
"Last year Dortmund made it to the final and I got to watch my former team-mates play there, so this time I want to have better memories of the tournament. [If Manchester United get through I'd like to face] Dortmund or Barcelona. I'd like to play against Messi and Iniesta.
"I used to play for Dortmund, I have friends there and the fans know me so I want to experience that dread of going to that stadium as the away team and I'd like to see how Dortmund would react.
"Even if they boo me, I'd be happy because it shows they recognise me. Of course I'd also look forward to meeting all the players and coaches and being in town again.
"Barcelona are playing the best football in the world so that's the most important thing. Iniesta is my ideal player; I've watched him throughout my career and hoped to be like him. It's fun to watch him play and that's the kind of football I'd like to play."